3.1.

Cold Telescope

The mirror temperatures of $\le 100\mathrm{K}$ required for astronomical background limited observations out to $5\mu \mathrm{m}$ (Fig. 5) can be achieved passively, as demonstrated by Herschel ($\sim 90\mathrm{K}$), JWST [42 K at the time of writing), Planck²² (36 K), Spitzer²³ ($\sim 30\mathrm{K}$), and WISE²⁴ ($\sim 75\mathrm{K}$) in their postcryogen phases]. ATSA is designed for passive cooling, taking advantage of the stable thermal environment at Sun–Earth L2 and using a sunshield that covers one side and the bottom of the spacecraft, while allowing the rest of the structure to radiate to cold space. Extending the sunshield beyond the SM on the Sun side forms a “sugar scoop” or scarf. This provides thermal and optical protection for observing angles ranging from anti-Sun to 40 deg from the Sun. On the opposite, shaded side, the shortened barrel exposes much of the PM and barrel interior to cold space, improving thermal radiation. The thermal design challenge is to balance the thermal input from the sunshield and the need to dissipate heat from on-board electronics. Radiators take up cold-exposed area and so low-power use is desirable. The thermal design and predicted performance of ATSA are detailed in Sec. 3.4.

3.2.

Mission Architecture

ATSA comprises two spacecraft, one carrying the telescope and science instruments, the other carrying a starshade 72-m-in diameter. Stowed into a package 7.81 m in diameter by 13.63 m high [including the launch vehicle adaptor (LVA)], the 6-m ATSA telescope can be launched into orbit at Sun–Earth L2 within the shroud of the SLS Block 2, 10 m $Ø$ payload fairing (PLF) long²⁸ launch vehicle or the SpaceX Starship+5-m extension.^29,30 Depending on the launch vehicle, the telescope is then boosted to Sun–Earth L2 or carried there within the Starship bay. The starshade inner disc is folded and the petals rolled into a cylindrical package (see the HabEx report² for more detail on the method) that measures $\sim 8.0\mathrm{m}$ high by 4.6-m diameter. Here we adopt the 72-m starshade package initially developed for HabEx (that mission concept eventually adopted a 52-m shade). Deployed, the starshade has twenty eight 16-m long petals arranged around a 40-m diameter inner disc. Although adequate mass capacity exists on the Starship to co-launch the starshade with the telescope, there is inadequate space and so the starshade would launch separately on a second Starship vehicle, using the standard fairing. For an SLS option, the starshade would utilize the SLS Block 1B Cargo with the 8.4-m PLF short-concept fairing. This two-launch mission concept gives a great deal of flexibility in scheduling, both during the development and science phases. Note here also that the starshade configuration could be adjusted to fit into a shorter, squatter cylinder by increasing the number of petals. Choosing 36 rather than 28 petals and assuming the same package volume would reduce the height to around 6.2 m and increase the diameter to around 5.2 m. Then stacking the starshade and telescope could potentially allow a single launch. More analysis would be needed to verify that.

The two spacecrafts are initially placed into similar halo orbits utilizing ground-tracking facilities. Before arrival at L2, the telescope sunshield and solar panels are deployed and the scarf cover is kept in place. Scarf deployment occurs in two separate one-time events as shown in Fig. 8. The sunshield deploys first to a fixed configuration. The scarf is rotated into position and locks to the barrel. After latching, the heaters and motors will not be reused and their wiring harnesses will remain benign. The sunshield interface between the scarf and barrel is an SLI labyrinth interface, with shield plies interleaving without contact, similar to the SLI labyrinth interface used to protect the support structure of the JWST star tracker after deployment. After arrival, the telescope cover can be opened and folded away, as shown in Fig. 9. The cover is designed to deploy and restow and is folded when latched against the barrel to free as much area as possible for the radiator panels. Deployment is in a single-direction actuation, similar to common solar arrays and only slightly more complicated with a restowing requirement. The solar panel extends the length of the barrel, split at the scarf joint. Latching electrical connectors carry power between the sections.

Fig. 8

(a) Telescope stowed configuration with scarf and cover in place and sunshield and solar arrays stowed. (b) Deployed configuration with scarf and cover unfolded and sunshield and solar arrays deployed.

Fig. 9

(a)–(e) Telescope in the stowed configuration with scarf and cover in place and sunshield and solar arrays stowed. Scarf folds back and sunshield and solar panels are deployed. Telescope primary mirror cover opens and folds up close to the barrel. The lower sunshield closeout to the bus is not shown here.

Deployment of the starshade is described in Sec. 4. After check-out, its laser beacon is acquired by the telescope in the wide field camera.

Starshade relative position data acquired optically on the telescope are relayed to the starshade via an S-band link and the starshade then performs any required maneuvers. The basic telescope and starshade system design parameters are shown in Table 1, which shows both launch vehicle options.

Table 1

Telescope and starshade system design parameters.

The telescope scarf permits observations as close as 40 deg from the Sun. The plane of the starshade can be positioned so that its normal is up to 85 deg from the Sun, so these two angles define the edges of the instantaneous FOR in starshade mode. As the Earth orbits the Sun, starshade observations can cover all of the sky except for small regions within 5 deg of the north and south poles of the ecliptic. For general science observations, the telescope can point up to 180 deg away from the Sun so that for general astronomy, most of the sky can be accessed at any time, the exception being the conical region within 40 deg of the Sun.

Since the telescope relies on passive cooling to reach its working temperature, the telescope barrel is partially wrapped by a five-layer sunshield as shown in Figs. 8Fig. 9Fig. 10–11. The sunshield is terminated on the bus as shown in Fig. 10, allowing observations with the Sun at the nadir angle. One solar array is placed along the length of the barrel on the outer spine of the sunshield (and split at the scarf joint), and the second solar array is located on the nadir side of the bus. The instruments are positioned behind the PM and arranged so that focal planes that need to be cooled are positioned near external radiators on the shaded side of the telescope and cooled passively, eliminating the power needs, thermal loading and vibration associated with cryocoolers. Figure 11 also shows the secondary mirror support struts within the barrel. The temperature at the top of the struts and therefore of the secondary mirror is about 60 K.

Fig. 10

The base of the telescope instrument bay and the bus section, showing the closure of the sunshield onto the bus, allowing observations with the telescope pointed directly away from the Sun. The keyhole-shaped objects are vents through which purge gasses escape before and during launch.

Fig. 11

ATSA thermal configuration. A five-layer sunshield protects the barrel, which is free to radiate to space on the shaded side. Arranged at the base of the barrel are radiators for cooling the electronics and the science focal planes.

ATSA, like HabEx, uses microthrusters for attitude control rather than reaction wheels. Microthrusters produce extremely low vibration,² with noise power spectral density of $0.3\mu \mathrm{N}{\mathrm{Hz}}^{-1/2}$, as much as four orders of magnitude lower than reaction wheels. The low vibration induced in the telescope structure by the attitude control system (ACS) results in minimal dynamic distortion of the wavefront.

ATSA’s science instruments include an ultraviolet spectrograph [multiobject ultraviolet spectrograph (MOUS)], a general purpose camera [multiobject visible-infrared spectrograph (MOVIS)], and a starshade instrument [exoplanet range extended starshade (EXPRESS)]. In addition, the telescope carries two focal planes for attitude control during science observations. Each instrument (with the exception of MOUS) has multiple internal optical paths and detectors. We refer to these paths as “channels.” The channel comprises the entire optical path from PM to detector, so that all channels share the telescope primary and secondary mirrors.

The starshade creates a shadow area within which the contrast ratio meets the ${10}^{-10}$ required for exoplanet science, accommodating the telescope aperture and the formation flying radius. The starshade is of the numerically optimized type³¹ and the high-suppression region (Fig. 12) extends from 300 to 1000 nm at the nominal working distance of 120 Mm, providing a 108% working bandwidth and a 51-mas IWA (given as ${\mathrm{IWA}}_{0.5}$) (${\mathrm{IWA}}_{0.5}$: the angle at which the planet signal drops by one half from the unobscured case). As shown in Table 2, this band can be moved to shorter wavelengths by increasing the starshade range from the telescope or longer by bringing the starshade closer in proportion to the desired center wavelength. Figure 12(a) shows the high suppression regions corresponding to those operating ranges.

Fig. 12

(a) Contrast against wavelength for different starshade ranges. With the starshade at 120-Mm range, the blue curve shows the stellar contrast in the “visible” 300- to 1000-nm science band. To either side of that band the starshade “leaks” starlight, which can be used for starshade formation flying control. The green and red curves show the contrast for the IR1 and IR3 science bands, illustrating complete coverage of the spectrum. For clarity, the UV and IR2 bands are not shown. (b) The appearance of the starshade at the ATSA focal plane in thermal emission as the starshade range varies. The plot shows the mean profile (as the starshade rotates) of the thermal flux, taking into account the petal shape. The thermal flux increases as the maximum science wavelength increases from 2500 to 5000 nm in 250 nm steps. The starshade temperature is 100 K. ATSA resolves the starshade so that the center of the thermal PSF is flat, with the Airy rings seen extending outward.

Table 2

Example starshade operating bands, ranges, and dimensions.

3.3.

Optical Telescope Assembly

Figure 13 shows the principal components of the flight system, consisting of the optical payload and its associated instruments and the standard bus parts. The optical telescope assembly (OTA) is formed by the 6-m-diameter PM and its underlying aft metering structure (AMS), three struts connecting that structure to the secondary mirror, and the secondary itself. Twelve outer segments of the PM (Fig. 7) each cover 30 deg of arc with 1285-mm radial extent, and six inner segments cover 60 deg of arc with 1390-mm radial extent. The central hole is 600-mm-in diameter. The gap between segments is 25 mm except where the surface is penetrated by the three secondary mirror struts, in these locations, the gap is 100 mm. Each PM segment, made of silicon carbide (SiC), contains an array of figure control actuators (FCAs) enabling the surface figure to be finely controlled. The segment is mounted via active bipods to the AMS, providing motion in six degrees of freedom (DoF). Segment area is $\sim 1.5{\mathrm{m}}^2$ for both inner and outer segments, a size within the current state of the art. Table 3 shows the mass breakdown of the PM and its components. The total areal density is $30.8\mathrm{kg}{\mathrm{m}}^{-2}$. JWST’s PM segments have an areal density of $\sim 30\mathrm{kg}{\mathrm{m}}^{-2}$, greater than ATSA’s segment areal density of $\sim 23\mathrm{kg}{\mathrm{m}}^{-2}$. JWST segment areal density had been increased during the design phase to meet stiffness needs under launch loads. JWST’s and ATSA’s total PM assembly masses cannot yet be directly compared, since ATSA’s AMS mass has not been detailed, but we would expect comparable total mass.

Fig. 13

The principal components of the flight system showing the payload and bus systems. K-band and S-band antennas, respectively, allow communication with the ground and the starshade spacecraft.

Table 3

Mass breakdown of the primary mirror assembly.

The PM segments have solid-state electroactive ceramic actuators embedded in their isogrid open-back structure. These surface-parallel actuators can correct large figure errors with accuracy depending partly on initial figure quality and partly on actuator density. This approach borrows the SiC substrate and basic design demonstrated through the development and testing of numerous “actuated hybrid mirrors³²” (AHMs), achieving 15-nm RMS SFE for mirrors up to 1.35-m size, as illustrated in Figs. 14 and 15. Actuators are placed within the ribs of the mirror backing structure, and as seen in Fig. 14, each segment contains a large number of possible locations. The WFE is inversely proportional to the density of actuators,³³ which also determines the upper limit of surface spatial frequency error that can be corrected. In-service SFE requirements will determine the final design of ATSA mirrors. The need to correct fabrication residuals and cool-down thermal deformations, as well as control mid-spatial frequency figure, will set the number and locations of the SFAs. The AHM mirrors demonstrated the ability to correct low-spatial-frequency figure errors by a factor of more than 100, from the $\sim 2\text{-}\mu \mathrm{m}$ RMS incurred by facesheet bonding strain to $\sim 15\text{-}\mathrm{nm}$ RMS (Fig. 15). The ATSA mirrors are expected to have lower initial SFE, as they will be polished to shape rather than bonded to a preform. Also the cool-down deformations of SiC substrates have been shown³² to be small ($\sim 30\text{-}\mathrm{nm}$ RMS). Assuming the initial figure error were specified as 100-nm RMS, a correction capability similar to that that AHM demonstrated would reach single-digit final RMS SFE, even with fewer actuators. More actuators mean greater correctability of initial errors, relaxing initial figure requirements. More actuators also mean lower amplitude residuals at higher spatial frequencies. By varying the rib structure and the numbers of actuators, the required wavefront conditions can be met by design.

Fig. 14

SiC mirror from a technology development program showing (a) the ribbed backing structure and (b) the mirror surface. Actuators push or pull on the backing structure causing localized bending of the surface. The diameter is 1.35-m point-to-point.

Fig. 15

The effect of actuators on the mirror figure. (a) Single actuators influence the wavefront both locally and globally. (b) The test mirror surface figure error before correction, which was dominated by release of the strain incurred by bonding the nanolaminate facesheet to the substrate. (c) The surface figure error after correction, showing two orders of magnitude improvement from $1.88\mu \mathrm{m}$ to 14 nm RMS figure error.

ATSA’s mirrors depart from the AHM formula in two respects. First, using a polished layer of Si as the reflecting surface rather than a replicated nanolaminate metal foil, better thermal deformation properties are obtained. Initial figure errors will be much reduced at room temperature, compared to the AHMs (Fig. 14), which exhibited 1 to $2\mu \mathrm{m}$ initial figure error caused by release of nanolaminate bonding strain. The Si facesheet provides an isotropic surface layer that enables polishing to meet UV surface requirements, targeting a microroughness level of under 5 Å. Second, ATSA’s mirrors will utilize cryocapable PZT actuators rather than PMN electrostrictive actuators, providing control authority both at room temperature and at the target operating temperature. Cryogenic testing of SiC substrates shows that cooling the mirror itself to 100 K or lower can be done without significantly degrading figure quality.³⁴ Cryocapable actuators have been characterized at temperatures as low as 25 K.^35,36

The PZT SFAs are installed so that they impart near-zero strain in their zero-volt state at room temperature. The actuator–substrate attachments are also designed to compensate the thermally induced differential strain when the mirror is cooled to its intended operating temperature. This is achieved via a “reentrant” clip constructed from a material with CTE dissimilar to the substrate/actuator, counteracting the relative mismatch in thermal expansion. This approach minimizes thermally induced figure changes and allows the telescope to be operated both at room and cryotemperatures and meet the PM performance targets of 20-nm RMS WFE at both temperatures. The basic principle has been demonstrated²⁷ at the 15-cm scale using a 12-actuator cryogenic active mirror, testing at temperatures ranging from room temperature down to 28 K. The technology readiness level (TRL) of the AHM mirrors is TRL5, but the athermalization, Si-cladding, and specific actuator implementation designs for full-scale ATSA mirrors need demonstration. The current status of ATSA segments is TRL3.

The PM segments are attached to the AMS backplane via the RBAs: linear actuators arranged in a hexapod configuration to provide six DoF of motion control. The SM is also attached via RBAs to its support struts. Based on those used on JWST, the linear actuators have nanometer precision and several millimeter range.

Telescope pointing is maintained by the ACS operating together with the fine guidance system (FGS), inertial measurement unit (IMU), and star trackers (Fig. 16). The FGS and star tracker utilize different guide stars, with the FGS forming the higher-precision component. The ACS commands the microthrusters to maintain pointing during observations. For large moves, the ACS commands the reaction control system (RCS) thrusters.

Fig. 16

Elements of the ACS: The FGS operates in conjunction with the IMU and star trackers to provide pointing and angular rate information. The ACS controls spacecraft pointing to match a target supplied from the ground using either microthrusters or RCS thrusters depending on the operating mode: science or slewing.

A TCS ensures adequate telescope thermal stability for many hours of observations. The TCS maintains the temperatures of the mirrors, AMS, optical benches, and bus, activating heaters as required. External radiators reject heat from the instrument focal planes, instrument electronics, bus electronics, and equipment.

The PM is cooled passively by radiation to space and to the cold side of the shroud. To maintain thermal control, a low-mass thermal shield backs each segment, connected at the bipod attachment points.

Beneath the segments, the AMS provides a second thermal shield against heating from the spacecraft bus. The segment figure-control actuators are high-resistance loads with low-power consumption. Each presents a heat load of about $100\mu \mathrm{W}$ to the mirrors, which the thermal model (Sec. 3.4) showed to be negligible.

The AMS panel is connected via a kinematic hexapod to the payload interface panel (PIP), in which the spacecraft electronics and systems are attached. Figure 17 illustrates the layout. The barrel, which surrounds the telescope instrument bay, the mirrors, and the bus, is a stiff honeycomb structure mounted to the PIP. The design ensures that the barrel, telescope sunshield, and solar panels are disconnected from the optical metering structure except through the PIP itself. The instrument bay is located above the PIP, whereas the bus is located below. The instrument bay is enclosed by the barrel and the PIP and AMS panels, with the instruments themselves mounted to the AMS panel. The primary optical metering structure consists of the AMS panel, PM hexapods, and the SM tripod struts, stiffened by the laser metrology (MET) system and partially isolated by the active hexapod attaching the AMS to the PIP. The instruments are individual subsystems, each of which includes a separate thermal environment for the optics enclosure and for the isolated electronics that are close-coupled with minimal cable lengths. Radiator panels are close-coupled to instrument detectors and detached from the barrel, eliminating thermal strains, and dynamic coupling.

Fig. 17

Schematic view of the bus and payload. The PIP carries the spacecraft bus, the telescope barrel and, via hexapods, the telescope optical system. This arrangement partially isolates the optical system from disturbances induced on the barrel and bus by providing a limited connection between the components. The secondary mirror is also attached to the AMS via struts (not shown here) with active control of position.

The $f/1.09$ PM’s central aperture allows light reflected from the on-axis secondary through to the instrument bay behind the AMS. The secondary mirror has an optical clear aperture of 562 mm; an optical scraper that creates a clean edge around the mirror brings the obscuration up to a diameter of 600 mm. All mounting structure for the secondary is behind the mirror, so as not to infringe upon the telescope aperture. In addition, three corner cube retroreflectors (part of the laser metrology truss discussed next) are face-mounted around the secondary between the clear aperture and the physical edge. Spaced 6000 mm from the primary, the secondary mirror is rigidly connected to the AMS via three struts, with actuators allowing active position control. The various instruments have either a tertiary or both a tertiary and quaternary mirror to provide the required wavefront qualities.

3.3.1.

Laser metrology and wavefront control systems

The WFC system (Fig. 18) maintains the telescope in its design optical configuration, following postlaunch alignments. Onboard functions run continuously, operating the SFAs, RBAs, and laser truss metrology as needed. Telescope geometry is controlled by the laser truss metrology system (MET),^37,38 which consists of a number of laser distance gauges (LDGs)—compact heterodyne interferometers. Free-space laser beams from transmitter/receivers mounted to the PM segments are launched to three corner cubes mounted around the SM. (There is an ideal corner–cube–launcher geometry and additional retroreflectors at M2 might prove beneficial in a final design). MET measures the distances between each of the segments and the secondary mirror. By making six measurements per segment, the segment position and angular orientation (“pose”) is determined. Figure 19 illustrates the layout. For clarity, the beams from only two segments of the PM are shown, but every segment carries six transmitter/receivers, located in three places. Similarly, a further six LDGs are mounted in a triangular configuration on the relay optics mounting structure, positioned directly below the AMS aperture and illuminating the three SM corner cubes. Thus the relative pose between the SM, the PM segments, and the relay optics can be measured to nanometer precision. The combined set of measurements enables precise monitoring of the telescope geometry. Using active relative position control of the PM and SM optics, effects such as long-term moisture desorption and short-term thermal expansion and contraction of the optical system can be eliminated.

Fig. 18

Active WFC system. On-board functions (green boxes) run continuously to stabilize the optical alignments against slow, mainly thermally driven disturbances. Ground processing functions (yellow box) are carried out intensively early in the mission to initialize the telescope optics and then only very occasionally after that to compensate laser and figure drift effects.

Fig. 19

Illustration of the laser metrology system. (a) Three or more (see text) retroreflectors attached to M2 reflect the metrology lasers back to their respective transmitter/receivers. (b)–(d) Six beams (cyan) are launched from the AMS (partly hidden by the primary mirror) through the central aperture of M1; six beams launch from each of the inner mirror segments (red, one segment set only shown); six beams launch from each of the outer mirror segments (green, one segment set only shown). Adding the remaining 16 segments, a total of 114 beams is launched and returned.

The compact LDG beam launchers³⁸ (transmitter/receivers) fit in the gaps between segments. Figure 20 illustrates the transmitter/receiver concept. A single input laser beam is split into two branches and fed to modulators, creating two beams with a small difference frequency. These beams are routed as shown in the transceiver and two outputs are produced, one modulated at the difference frequency and the other at the difference frequency with a phase difference. This phase term is proportional to the distance change between the transceiver and the corner cube retroreflector placed on the target. A total of 114 transceivers is used, derived from three or more lasers using beam splitters to multiplex the laser sources. Only a few milliwatts total laser power is needed to produce all the beams. The ultrastable laser sources needed are in the development for space systems, such as GRACE-LRI.^39–41 ATSA’s metrology beam launchers and adjacent fibers will operate at 100 K. This technology we assign TRL 4 (reduced from TRL 5 in the HabEx study) so that demonstration of $\sim 1\mathrm{nm}$ performance in cold conditions is required to enable advancement to TRL 6.

Fig. 20

Layout of the laser transceiver system. Two frequency-shifted laser beams (local and target) enter a beam-combination module that forms a transmitter/receiver. The target beam is transmitted to a corner cube retroreflector on a remote target and returns to be combined with the local beam. Internally, the local and target beams are also combined to form a phase reference. Two intensity-modulated output beams are detected and the phase shift between these outputs forms the metrology signal. The laser source is multiplexed via a series of inline fiber splitters to a number of transceivers.

MET signals, produced at 1 kHz with $\sim 1\mathrm{nm}$ accuracy, are processed in a control system that continuously compares the pose of each optic to a commanded target pose. Pose errors are corrected by the RBAs at a 1-Hz bandwidth. This provides noise reduction by signal averaging; nanometer-level pose errors translate to picometer-level WFE performance over time scales of tens to thousands of seconds. Such performance levels are within the state of the art^37,38,42,43 with optical sensors sometimes combined with other types. The MET-based OTA rigid body control system also provides a highly accurate servo control mode, where true optical pose commands, such as defocus, can be executed with nanometer precision in closed loop.

3.4.

Thermal Design

The general scheme for the thermal layout is shown in Fig. 21. Solar illumination heats the structure and, since sunlight impinges directly onto the outer barrel assembly (OBA) shield hinge-line, additional shields are incorporated to minimize parasitic heating at this junction. The main OBA shield is made up of five discrete shields. Each shield is angled away from the next to operate as a V-groove radiator, causing photons to bounce between the specular surfaces, propagating to free space from the side of the shield. Internal shield layers are assumed to be 7 mil Kapton film with an IR emissivity of 0.02. The edges of the internal shield layers with a potential view to any solar heating have an additional outer layer of silver teflon co-cured to the Kapton. The outermost layer of the shield is assumed to be completely silver teflon. The OBA spine shields use the same materials (except for the final solar array layer). Figure 22 shows predicted OBA shield temperatures as a function of solar vector to OBA angle. Table 4 shows the driving temperature requirements. Where no particular requirement was levied, this table shows an ellipsis.

Fig. 21

The schematic layout of the thermal system. Heat pipes conduct heat from the payload adaptor plate and the AMS to radiator panels. Within the instrument bay itself, the instruments are cooled using a two-stage system (or a single stage for the warmer instruments) with a warmer panel set behind and extending beyond a colder panel. The warmer panel is connected to the instrument enclosure via heat pipes and the colder one to the detector via a thermal strap. MLI is added around the instruments and any free space optical paths as needed to maintain isolation.

Fig. 22

Thermal model of the sunshield, solar arrays, and telescope barrel assembly. The angles represent the solar vector shown with the sun impinging at the side (0 deg) through to the base (90 deg). The five-layer solar shield provides excellent thermal shielding and much of the barrel is below 100 K at all Sun angles.

Table 4

Temperature requirements.

Both the inner parts of the barrel and the outer parts on the anti-Sun side have high emissivity to ensure excellent heat exchange with cold space. Since the barrel is short with a relatively long scarf, it provides a direct view of cold space for much of the interior of the barrel and at least a partial view for the rest. Figure 22 shows the results of thermal modeling of the barrel at a range of Sun angles. With the barrel side-on to the Sun ($\theta =0\mathrm{deg}$), the superior surface of the solar array reaches 361 K and the sunshield reaches as much as 280 K, while most of the protected parts of the barrel, instrument payload volume, and bus are well below 100 K. At the nadir angle ($\theta =90\mathrm{deg}$), the base solar array reaches $\sim 300\mathrm{K}$ and the barrel warms slightly. The temperatures of the primary and secondary mirrors and the instruments are shown in Fig. 23 and the model detail of the primary mirror is shown in Fig. 24.

Fig. 23

Thermal model of the OTA and instruments with AMS removed for clarity. The primary mirror is at $\sim 100\mathrm{K}$ (details shown in Fig. 24) and the instruments exhibit a range of temperatures depending on the Sun angle. Detectors are uniformly cold (cyan colors at the narrow ends of the boxes). The UV instrument, which does not have specific cooling requirements, is warmest at up to 158 K. At the nadir angle, there is some general warming of the instrument bay. Although this is currently considered acceptable, if necessary this could be addressed by adding a small sunshield at the side of the base opposite the sunshield closure.

Fig. 24

Primary mirror segment temperatures as a function of solar angle. As anticipated, the nadir angle presents the worst case, with some segments warming to as much as 105 K with the target being an overall effective temperature of 100 K or below. These warmer segments do not cause requirements to be exceeded, however, since the radiation from the primary mirror as a whole is equivalent to 87% of the radiation from a uniform 100 K primary.

Beneath the AMS, the instrument boxes are passively cooled via heat pipes connecting to external radiators on the cold side of the barrel. The most thermally sensitive instruments are located on the cold, anti-Sun side of the telescope, with focal plane detectors positioned as near as possible to their radiator panels on the outside of the barrel. The uppermost panels cool the primary mirror surface control electronics, individual detectors, and the instrument optics and electronics in the instrument bay. The lower radiator panels dissipate heat from the power supplies and bus subsystems. The entirely passive thermal system eliminates the need for staged isolation with active cryocoolers, allowing bus mass to be reduced and vibration sources removed.

A passive radiator is included for each cold instrument (Fig. 25) and the attachments allow for differential motion between the OBA and radiators during launch. Mounting bipods protrude through apertures in the OBA allowing radiator installation after instrument installation. This configuration allows thermal testing of each instrument as an independent unit. Flexible graphite straps run directly between the focal planes and second stage of each radiator. Each of these passive coolers is sized to reject up to 1.5 W of focal plane array (FPA) dissipation at 55 K. This assumption is conservative for current focal plane selections. Inside the instrument bay, individual instruments are contained within enclosures mounted to the AMS optical bench. Each detector is close-coupled via short links to one of four $2.7\text{-}{\mathrm{m}}^2$ two-stage radiators. Figure 25 shows the enclosure temperatures of key instrument channels and their respective radiator panels.

Fig. 25

(a) General thermal view of the instruments beneath the AMS. The AMS temperature is $\sim 90\mathrm{K}$, and the MOUS temperature is $\sim 135\mathrm{K}$. (b) The instrument enclosure temperatures for the cooler channels and detectors together with their detector radiator panels.

The heat load from ATSA avionics is substantial. A 35-W avionics chassis is allocated to each primary mirror segment (630 W total). These chassis are attached to three separate thermal pallets (mounted via titanium flexures to the AMS) carrying embedded ammonia constant conductance heat pipes (CCHPs) (Fig. 21). The pallets are thermally linked via three compact ammonia loop heat pipes (LHPs) to two warm radiators mounted onto the OBA (Fig. 26). Both radiators have internal ammonia CCHPs to increase radiator efficiency. Survival heater circuits are placed on both the avionics pallets and radiators to prevent ammonia from freezing when avionics are not operating. The three segment drive avionics pallets and the larger wiring harnesses are fully enclosed with multilayer insulation (MLI) (effective $e^{*}$ of 0.03), and the temperature of the electronics is low (250 K nominal) to prevent heat transfer to the primary mirror. A high-quality MLI enclosure is critical here ($e^{*}$ of 0.03 is assumed).

Fig. 26

(a) Circular heat pipe layout at the AMS. Two rings connected to external radiators (b) provide cooling for the AMS-mounted electronics. (c) A similar layout at the payload adaptor plate provides cooling for the bus electronics.

Instrument avionics dissipate 550 W spread over 23 separate avionics chassis. These avionics boxes are for focal plane interface electronics, motor drive electronics, solid-state recorders, GNC components, etc. The boxes are arranged on five separate avionics pallets with embedded CCHPs. The pallets are either suspended from the AMS or supported from the PIP to minimize harness lengths and linked to each other by dual-bore CCHPs to the PM drive electronics pallets. Two external radiators mounted to the OBA are connected via flexible LHP assemblies. Each avionics pallet is fully enclosed with MLI and kept cool (250 K).

To isolate the internal spacecraft bus from the external environment and to minimize thermal gradients, much of the spacecraft bus will be blanketed. MLI blankets and thermal isolation washers will be utilized between the Sun-facing solar array and the sunshield, and between the nadir mounted solar array and the external radiators, thermally isolating these heat sources from the bus. Blankets and conductive isolation ensure no net heat exchange with the instrument deck. Cooling for bus subsystems mounted inside the bus will be provided by two $3.1\text{-}{\mathrm{m}}^2$ radiators on the bus cold side. The radiators are connected to set of jumper heat pipes and these jumpers are connected to circular ammonia-filled, constant-conductance heat pipes embedded into the base mounting panel. The pipes ring the inside of the bus, providing easy access to cooling and are connected to heat sources, such as batteries, power conditioning units, and bus electronics. Figure 26 illustrates the concept.

Cooling for the instrument panel (the AMS) is provided in a similar fashion. Two $2.7\text{-}{\mathrm{m}}^2$ radiators for focal plane electronics and two $2\text{-}{\mathrm{m}}^2$ radiators for segment drive electronics are placed on the spacecraft’s cold side and connected via jumper heat pipes to a set of circular ammonia-filled, constant-conductance heat pipes embedded into the AMS panel separating the instrument bay from the bus. Miscellaneous heat sources, such as filter selection motors, are connected to the heat pipe ring for cooling. Heat pipe and radiator sets may be combined via manifolds to offer higher margins for heat rejection area.

3.5.

Bus Architecture

The bus equipment is placed in a tapered cylindrical volume created by the PIP and the LVA. The base of the volume is formed by the nadir solar array, located immediately above the launch vehicle interface ring that provides the interface to the launch vehicle via a payload adaptor fixture (PAF). After launch, the payload separates from the launch vehicle at the PAF interface.

Figure 27 shows the telescope stowed within both the Starship shroud (+5-m extension) and the proposed SLS 10-m long fairing. Dimensions are based on the SpaceX Starship Users Guide³⁰ and the SLS Mission Planner’s Guide.²⁸

Fig. 27

Schematics showing possible launch vehicle fairing options. (a) The telescope within the envelope of the proposed SLS PLF 10-m long, leaving about 0.9 m of height to spare. (b) Within the SpaceX Starship +5-m extension shroud. In (b), the thick green lines delineate the dynamic envelope. A plan view is overlaid at top, illustrating the negotiable volumes (blue areas) within the fairing. The stowed telescope fits within the cylindrical section of the fairing with 0.52-m height to spare. More margins exist within the conical section of either fairing.

The bus includes the following.

Figure 28 shows bus equipment mounted on the cruciform panels, the sloping walls of the LVA cone and the nadir panel. Beneath the circular panel that closes out the bottom of the bus volume at the LVA ring is the nadir solar array, which also contains the high-gain antenna (HGA). The central cone from the LVA to the PIP is a solid layup of graphite composite. The cruciform, PIP, and nadir structural panels are sandwich-structured composite face sheets and aluminum honeycomb core with thickness adequate to provide stiffness against launch loads. Metallic and composite secondary structures and bracketing support the solar panels, propellant tanks, and bus subsystems. Primary load paths pass from the primary mirror through the AMS hexapod and into the PIP, and from the telescope barrel to the PIP, down to the LVA and PAF via the stiffened cone. The stiffening shear walls, cone, and panels of the bus support the 12,745-kg vehicle dry mass with a good portion of the propellant mass being transferred directly to the LVA ring via the nadir plate.

Fig. 28

Bus model showing tanks for 2660-kg hydrazine and 105-kg colloid propellant and volumes for the control valves (blue boxes) and fill and drain valves (gray boxes). Spacecraft electronics are mounted outside the cone, enabling direct cooling via external radiator panels.

3.6.

Propulsion

Two independent propulsion systems provide maneuvering and attitude control. Monopropellant thrusters provide large thrust enabling rapid slewing, whereas colloidal microthrusters handle the solar torques during science observations. The monopropellant system consists of one 440 N main engine (e.g., Rocketdyne MR-104J, $I_{\mathrm{sp}}=220\mathrm{s}$), four 22-N thrust vector control engines (e.g., MR-106L) enabling three-axis control, and sixteen 4-N attitude control engines (e.g., MR-111G), enabling six-axis control. A monopropellant system is preferred over a bipropellant system because there is only a single component to refuel, but it carries a mass penalty owing to a typically 30% lower specific impulse.

By removing the reaction wheels commonly employed for attitude control on spacecraft, ATSA benefits from an extremely low vibration environment, while retaining exquisite attitude control. Microthrusters of different types have flown on both Gaia⁵² (cold gas type with ${\mathrm{N}}_2$ propellant) and Laser Interferometer Space Antenna (LISA) Pathfinder⁵³ (electrospray with colloidal liquid propellant) and are in continuous development for use on other missions. The colloidal type provides much higher specific impulse (quoted values ranging from typically from 180 to a few 1000 s) than the cold gas type ($I_{\mathrm{sp}}\sim 60\mathrm{s}$) and is therefore specified for ATSA. Thrusts in the 10- to $100\text{-}\mu \mathrm{N}$ range are currently available with the thruster with 18 emitter heads developed for LISA. Thrust resolution is as fine as $0.1\mu \mathrm{N}$. Newer developments⁵⁴ promise 20 mN in a package measuring $\approx 180\times 180\times 45\mathrm{mm}$.

In an L2 orbit, solar torques will be $\sim 3.0\mathrm{mN}\mathrm{m}$, based on the solar photon flux, assuming 4.5 m between the centers of mass and pressure, 80% absorption on the solar arrays, and reflection of the remaining 20%. The ATSA telescope barrel has an area of about $18\times 7{\mathrm{m}}^2$ with the sunshield deployed. To avoid placing electrospray thrusters (which would need to be heated and have heated supply lines) along the telescope barrel, the thrusters are placed near the base, attached to the bus. A single unit of the experimental thruster would be capable of producing as much as 86 mN m of torque at this location, so four somewhat smaller units would suffice and provide control over roll, pitch, and yaw.

ACS monoprop thrusters are mounted in pairs at eight locations, four sites at 90-deg intervals around the exterior of the bus and an additional four around the barrel about half way along, providing adequate torque control. Sizing the propellant loads for pointing control, slews, TCMs, and stationkeeping for a 5-year mission (based on scaled-up⁵⁵ HabEx 4.0 figures) results in 2660 and 105 kg mass budgets for monoprop and colloid, respectively, before margin. Refueling ports utilizing Vacco type II resupply valves on the exterior of the spacecraft bus allow replenishment of consumables via robotic servicing to extend operations.

3.7.

Mass

The spacecraft wet mass with 43% margin applied is about 18,200 kg [see Table 5 for current best estimate (CBE) masses]. This is roughly 10% less than LUVOIR-B. More massive components of the OTA are the barrel, the primary mirror, the electronics, cabling, and AMS together with the sunshield and solar arrays. The bus mass is similar to that of LUVOIR-B. Propellant needs for insertion into and maintenance of the Sun–Earth L2 halo orbit are calculated by reference to LUVOIR-B, which assumed four mid-course correction maneuvers and subsequent orbital insertion at around 100 days and a 10-year mission. In this table, launch on the SLS Block 2 Cargo with the proposed 10-m PLF long fairing option and EUS providing lift to L2 is assumed. The amount of colloidal propellant on the telescope spacecraft is sufficient for 10 years of attitude control. After orbital insertion, the spacecraft has a beginning of life mass of 12,034 kg. In the case of launch on the Starship (capable of 150,000 kg to L2 after refueling in low-Earth orbit), payload hydrazine requirements could be reduced by as much as 674 kg, assuming the Starship vehicle is used to insert the telescope directly into its final orbit. The Starship would then return to Earth. Thus viable launch vehicle options are already at least in the concept phases.

Table 5

Mass summary budget assuming an SLS launch.

3.8.

Power

The power system consists of solar arrays, batteries, distribution cables, and interface hardware. Aft-mounted solar panels with area $29{\mathrm{m}}^2$ and barrel-mounted solar panels with area $23{\mathrm{m}}^2$ provide power. The aft-mounted panels are fixed, whereas the barrel-mounted panels are deployed after launch by extending them laterally. They provide a minimum of 3300 W when the telescope is pointed 40 deg from the Sun and 4200 W at 180 deg from the Sun. Peak power consumption of 3050 W occurs while science data are downlinked during observations (see Table 6). Lithium ion batteries with 3000 Ah capacity at 3 V provide 3 h of power after launch, maintaining capacity above 70%. The same battery system provides backup power in normal operation and in safe mode.

Table 6

PEL and summary budget.

3.9.

Communications

The communication system supports tracking for navigation via NASA’s Deep Space Network and downlinking of science data. The Ka and X bands ($6.5\mathrm{Mb}{\mathrm{s}}^{-1}$ and $100\mathrm{kbp}{\mathrm{s}}^{-1}$, respectively) are used for these communications. A single deployed, gimballed HGA mounted on the telescope bus enables science observations with simultaneous downlinking. (Alternatively, science data could be stored on board and down-linked periodically to avoid any issues with vibration from the gimbal. Another alternative would be two fixed phased array antennas enabling continuous vibration-free data transfer.) A link is provided between the telescope and starshade by an S-band patch antenna placed on the back of the secondary mirror. This low-bandwidth link (100 bps) conveys starshade formation-flying data and operation mode signals bidirectionally, as well as providing a time-of-flight measurement that enables starshade range sensing.

3.10.

Contamination Control

Buildup of contamination on optical surfaces, both particulate and molecular,⁵⁶ degrades optical performance. Particles on optical surfaces obscure, absorb, and scatter incident light, whereas molecular contaminants reduce signal by absorption, scattering, and thin-film interference effects. These effects accumulate with each successive optical surface, so that the total loss in the optical chain can be estimated by summing the loss at each element. Contamination tests^57,58 have shown the presence of polymerized materials on mirror surfaces that degrade performance in the UV.

Sources of particles include those shed from surfaces and from cleanroom personnel, together with general fallout in the cleanroom. Particles may redistribute during launch. Molecular contamination sources include manufacturing process residues, integration and test processes, material outgassing and redeposition, and deposition of propulsion byproducts. The resulting optical effects are strongly dependent on wavelength. They are most serious at shorter wavelengths but may be important at longer wavelengths too.

Contamination controls (CCs) are required for ATSA, both to limit degradation and also to recover from degradation if it occurs, so that the observatory can maintain its required performance throughout mission life. An effective CC program will have several elements, guided by quantitative per-element contamination budgets and designed using CC modeling incorporating molecular generation, transport and deposition, particle redistribution, and effects peculiar to the space environment.⁵⁹ As the design evolves, iterations of the transport model keep track of developments. These CC models and methods are grounded in the extensive experience gained on missions including Hubble, Galex, Spitzer, Herschel, and Planck.

An effective CC program thus begins during the project design phase with these main elements.

During fabrication, assembly, and test, contamination will be controlled by materials processing, cleanroom protocols, frequent cleanliness inspection and monitoring, and surface recovery cleaning protocols. As each assembly is closed out, cleanliness will be preserved using remove-before-flight and in-process protective covers, with gaseous nitrogen purge to instrument enclosures.

During launch the entire system will be kept above the dew point. Once in space, the mirrors and other optical surfaces will be kept warm by heaters, as the rest of the system cools radiatively. As the barrel and bus surfaces reach operating temperature, they act like a cryogenic vacuum pump to condense residual outgassed materials, trapping them away from the optics. After a suitable interval, the optics are allowed to cool to working temperature. This scheme has been used successfully by Spitzer and several other cryogenic missions.

Once in operation, performance will be monitored to detect any contaminant buildup. As needed, periodic decontamination operations will be conducted, using heaters to warm affected components, displacing any accumulated volatile contaminants onto much colder, nonoptical surrounding surfaces.

ATSA spacecraft design places the hydrazine monopropellant thrusters and the colloidal microthrusters at the base of the telescope barrel and on the bus, pointed away from the aperture. Then paths to the critical optical surfaces will pass via large, cold surfaces that trap contaminants. The very high-exit velocity and the very low volume of the microthruster propulsion also limits the potential for contamination. A detailed assessment of thruster plume dynamics will be conducted for ATSA, but the risk to the sensitive surfaces is considered low.

Any UV telescope must be carefully engineered to control contamination and ATSA is no different: it must reach orbit and operate with very little particulate or molecular contamination of its optical surfaces. What is different is its cold operational temperature and this is a significant advantage. By keeping all optics warm during launch and initial orbital flight, then letting the surrounding nonoptical structures go cold, ATSA has built-in traps for outgassed volatiles. As the optics are finally allowed to go cold, the adsorbed volatiles will freeze permanently in place on the trapping surfaces.

As an example, Fig. 29 shows the result of thermogravimetric analysis of outgassed materials from a commonly used RTV adhesive (S691).⁶⁰ A quartz crystal microbalance (QCM) is cooled to 80 K under vacuum (${10}^{-10}$ to ${10}^{-8}\mathrm{Torr}$) and allowed to accumulate material evaporating from a nearby piece of cured RTV, maintained at 333 K. After six days, the RTV sample is removed and the QCM is slowly heated over a period of 144 h, allowing the accumulated material (consisting of a wide range of chemical species, water being a major component) to evaporate or sublimate. This figure shows that below $\sim 120\mathrm{K}$, the evaporation rate is below ${10}^{-11}\mathrm{g}{\mathrm{cm}}^{-2}{\mathrm{s}}^{-1}$. This implies that, at these low surface temperatures, material exchange between surfaces is at extremely low rates and that clean optical surfaces will remain uncontaminated for long periods. A second implication is that local heating of contaminated surfaces can be employed to boil off material and trap it on surrounding colder surfaces. ATSA’s cold temperatures thus offer the potential for truly robust on-orbit CC.

Fig. 29

The outgassing rate of accumulated materials from a cold surface as the temperature is raised from 80 K over a period of 144 h (data adopted with permission from Ref. 60).

4.1.

Overview

The starshade provides exoplanet science capability from the near-UV to the MIR. Successful operation of the starshade at longer wavelengths requires the starshade to appear cool to the telescope, so that thermal radiation from the shade does not limit detection. Compounding this effect is the need to bring the starshade closer to make longer wavelength observations; the starshade is operated at constant Fresnel number given by $r^2/\lambda Z$, where $r$ is the radius of the starshade and $Z$ is the range. Having a reflective material on the Sun-facing side of the starshade, using multiple layers (rather than just three for HabEx) to form the optical shield (OS) and operating the shade at advantageous Sun angles to limit its illumination, all help to lower the starshade temperature. For example, with the starshade normal making an 80-deg angle to the Sun, the insolation is $4.4\times$ less than at 40 deg, reducing the shade’s absolute temperature by $\sim 70\%$. Figure 33 shows the effect on the AB magnitude of the starshade, with significant decreases in starshade brightness for Sun angles larger than 40 deg. Objects in an annular field almost perpendicular to the Sun-telescope line can be observed with a cool starshade and as the year goes by, most of the sky can be observed excluding the two circular areas 14 deg in diameter centered on the ecliptic poles.

4.2.

Starshade Deployment

After launch, the shroud is discarded and the second stage sets the trajectory toward L2. Once on track, the second stage is discarded and any required trajectory correction maneuver (TCM) takes place after an orbit determination undertaken within a couple of days. Immediately following launch the starshade bus is powered by solar panels [colored blue in Fig. 30(a)] mounted on the central hub. Starshade biprop thrusters (described below) are used for the TCM. The starshade is initially positioned into a halo orbit close ($\sim 100\mathrm{km}$) to the telescope, utilizing ground-tracking facilities. During the transit to L2, the petal unfurling system (PLUS) deploys the 28 petals and the inner disc is extended. Upon arrival, injection into the halo orbit (a low-thrust maneuver) is accomplished using the starshade thrusters. Each petal is 16-m long (Table 7) and the inner disc has a radius of 20 m, resulting in the 72-m diameter assembly (Fig. 31). As the disc extends, the petals unfold [they are folded face to face in pairs (see Fig. 30)] and two structural ribs on each petal fold out and lock into place. These ribs add stiffness by adding an out of plane component to the otherwise planar petal structure. The gaps between the petals at the root and the petal widths at the tip are about 4 mm. The inner disc carries additional flexible solar panels to power the spacecraft bus and its solar electric propulsion (SEP) system. Once deployed, the starshade rotates slowly at $2\mathrm{deg}{\mathrm{s}}^{-1}$.

Fig. 30

Starshade deployment sequence (26-petal SRM shade shown). (a) The starshade wrapped around the hub, held captive by PLUS. (b) PLUS, having unfurled the petals, separates from the starshade spacecraft and is discarded. (c) The central disc expands completing the deployment.

Table 7

RM12 Starshade specifications.

Fig. 31

One petal (the 3 o’clock petal) and inset, the proportions of the starshade. Petal base gaps and tip widths are $\sim 4\mathrm{mm}$.

4.3.

Starshade Design and Thermal Performance

The superior surface (Sun side) is covered in low-emissivity-coated Kapton to reject heat, whereas the inferior surface (telescope side) is covered with high-emissivity black Kapton. These two layers form part of the starshade’s OS, which has four additional layers to provide additional thermal isolation and also to protect against micrometeoroid strikes. Figure 32 shows the scheme. The OS is the main source of thermal photons from the starshade and one mechanism, thermal radiation between the layers, dominates. The OS as a whole has black Kapton layers that absorb light and heat, and other layers that reflect it. The net effect of the set of layers is to create a cold inferior surface that minimizes the thermal photon flux from the starshade, permitting observations into the MIR. At starshade angles of 40 deg to the Sun (measured from the normal), the temperature of the inferior surface is expected to be 101 K, while at 80 deg this drops to 69 K. Between these temperatures the photon fluxes at $5\mu \mathrm{m}$ observed from the telescope fall from 0.4 to ${10}^{-6}\mathrm{ph}{\mathrm{s}}^{-1}$ in a 10-nm bandwidth, low enough to permit science observations on exoplanet targets. Thus targets at higher celestial latitudes would be favored, but even those at 40 deg are possible. Figure 33 shows the thermal photon flux from the starshade, observed at the telescope, in terms of AB magnitude. A second, considerably weaker source of thermal radiation is discussed next.

Fig. 32

Multilayer insulation and OS. Low-density scrim separators keep the main elements apart while crinkling is used to separate the thinner layers.

Fig. 33

(a) Thermal photon flux as a function of starshade temperature, illustrating the critical importance of reaching a low temperature for observations at the longest possible wavelengths. Also starshade range as a function of the longest wavelength in the science band. (b) AB magnitude for thermal radiation from the shade at a temperature of 101 K, as a function of observing wavelength and solar incidence angle.

The whole OS assembly forms a barrier to micrometeoroids, which can make very small holes in the exterior surfaces. The majority of micrometeoroids do not penetrate the first layer of the shield. Larger particles are vaporized upon exiting the first layer and fail to penetrate the second. Only the largest particles penetrate the entire assembly of layers. In any case, starshade science observations are tolerant to at least $1{\mathrm{cm}}^2$ of direct through-holes.⁶¹ In addition, sunlight penetrates superficial holes and scatters within the layers, with a portion eventually emerging as an incoherent field from the inferior surface. The radiated amount depends on the hole area (conservatively assumed the same in each layer) and the absorption between each pair of layers, which is high because a large number of reflections is required to find an exit hole, as illustrated in Fig. 34. For small hole areas, the leakage is proportional to the fractional hole area and this leakage decreases geometrically as the number of layers increases. Even for high-reflectivity layers, such as the third through fifth layers, the multiple reflection terms (lower rightmost in the figure) fail to counteract this effect significantly. Thus the ATSA starshade is expected to appear extremely dark ($>70\mathrm{AB}$ magnitude) for transmitted sunlight at working range.

Fig. 34

Effect of holes from micrometeoroids in the starshade. Sunlight impinging on the top layer is largely reflected. Light trapped between the layers undergoes multiple reflections until it is either absorbed or transmitted through the lower layer (or back up to the layer above). Despite the high probability of multiple reflections, little light makes it through because of absorption.

Sunlight scatters from the starshade edges and a small fraction will enter the telescope, creating a background. For this reason, the edges are made very sharp ($<1\text{-}\mu \mathrm{m}$ radius), similar to a razor blade (although the angle is obtuse rather than acute). Edge scatter, arising both from diffraction and reflection, has been analyzed and measured^62,63 using prototype edges in the laboratory. Since the edges are sharp, the dominant scatter component is diffracted light. We term as “leading edges” those on which the sunlight impinges directly; the opposite edges we term “trailing edges.” The scattered light from the leading edges is strongly S-polarized, while that from the trailing edges is strongly P-polarized (as Sommerfeld⁶⁴ showed in 1895). The P-component may therefore be substantially removed by designing the petals to shade the trailing edges. At visible wavelengths, edge scatter is the strongest contributor to the background ($\sim 25\mathrm{mag}$), but it may be suppressed by applying coatings to the edges, a technology that is now being developed⁶⁵ and is showing suppression $\gg 5$ magnitudes. At longer wavelengths, the diffracted intensity will increase linearly with increasing wavelength. Additional analysis, coating development, and indeed testing will be needed to characterize starshade edge requirements for operation at these longer wavelengths.

4.4.

Starshade Bus

The starshade utilizes a conventional spacecraft bus (see Fig. 35) with the usual functions. The starshade hub structure resembles a large cable spool and is composed of a cylinder with flanges at each end. The cylinder is a strong honeycomb composite structure 1.8-m-in diameter and contains the bus, comprising the principal spacecraft systems as well as the hydrazine and xenon propellants. The starshade bus includes the following.

Fig. 35

The principal components of the starshade spacecraft. K-band and S-band antennas allow communication with the ground and the telescope spacecraft, respectively, while the beacon facilitates starshade acquisition after transit maneuvers.

The starshade’s hub structure attaches directly to the LVA ring via a payload interface plate (PIP) mounted on the lower flange. In turn, the LVA is mounted to the launch vehicle’s PAF, from which it separates after launch. Starshade launch loads are carried through the walls of the central spool-like cylinder section. The propellant tanks are positioned on the inside surface of the spool’s lower flange, providing a direct load path to the LVA. Two lightweight flanges extend to and retain the starshade PLUS interface structure (a combined deployment and constraint device—see description below), which in turn retains the furled petals. Just inside the petals, the disc’s rigid ring truss structure is folded concertina-fashion and within that ring, the OS forming the circular core of the starshade is folded in a spiralling origami “flasher⁶⁶” pattern. Flexible solar panels providing power to the SEP system are mounted to the superior surface of part of this OS. For deployment, after rotation of the PLUS, which releases the petals folded face to face in pairs, only one additional mechanism—a cable drawn in by a motor—is required to unfurl the starshade, extending the truss and unfolding the petals. Cables between the truss and the hub (acting like the spokes of a bicycle wheel) become tensioned during the final stages of deployment and stiffen the entire structure.

The bus equipment is mounted within the hub on the sandwich-structured composite of aluminum face sheets and aluminum honeycomb that form the upper and lower flanges. On the upper flange, structures and brackets support fixed low-voltage solar panels and electronics equipment. Propellant tanks are mounted on the lower flange, but thermally isolated to prevent a “hot spot” underneath the starshade. Excess heat from the warm propellant tanks is radiated at the cylinder sides, i.e., above the superior surface of the starshade.

The thermal subsystem maintains the bus equipment at correct flight temperatures. Approximately 150-W of heater power is required to maintain the propellant temperatures during normal operations; 30 W is required during launch, downlink, and safe modes. Thermistors measure temperatures and strip heaters provide heat where needed. The subsystem also includes MLI blankets to isolate the lower flange and variable-conductance heat pipes to bring waste heat to the radiator. Aided by the slow rotation that distributes the solar thermal load evenly, the starshade petals and much of the inner OS are thermally stable, with only small residual fluctuations from the rotation.

4.5.

Formation Flying

Under the influence of radiation pressure and gravity gradients, the starshade is continuously accelerated, but during science observations it must be maintained within a circular area of diameter 2 m, centered on the line of sight to the star. (The circle size is invariant with respect to starshade range.) This is done by periodically (∼every 10 min) and briefly ($\sim 10\mathrm{s}$) firing thrusters to project the starshade back up to the top of the control area and letting it fall back in a ballistic trajectory. During thruster firing, the starshade science instrument will have to be protected from the relatively bright thruster plumes, which are of apparent magnitude about 13. This is achieved by [as in the starshade Rendezvous Mission (SRM) concept] briefly switching the detectors to a fast readout mode during thruster firings. This is sufficient to prevent saturation and the formation of a persistent image. The other instruments are sufficiently far off-axis from EXPRESS that they could likely continue to operate undisturbed since thruster plumes are unlikely to pass through their fields of view. Exceptions may occur in cases where the plume passes through the FOV and the integration times are long. By keeping the thruster firing times short, the observation time is maximized and typically there will be several minutes of free flight between thruster firings.

To maintain the starshade on the line of sight, the starshade shadow is observed at wavelengths either shorter than or longer than the science band. Since the starshade is of the numerically optimized type (rather than the hyperGaussian⁶⁷), it blocks starlight very efficiently across the science band and leaks light at either end, as shown in Fig. 12. Thus when the starshade is operating in the near-IR band (750 to 2500 nm), a signal can be obtained at $\lambda \approx 600\mathrm{nm}$ or at $\lambda >4000\mathrm{nm}$). This signal consists of a shadow of the starshade, observable at the telescope entrance aperture. The principal feature is a residual spot of Arago, having a diameter approximately $d_A=r/(2F)$, with the starshade radius 36 m and the Fresnel number typically $\sim 8$ at the longest wavelength and therefore $\sim 32$ at the $\approx 600\mathrm{nm}$ leakage wavelength. The spot would be $\lesssim 0.6\mathrm{m}$ wide and 500 times fainter than the target star in a $\lesssim 100\mathrm{nm}$ bandwidth, quite sufficient for detection. By imaging the telescope entrance pupil onto a camera, the starshade position can be followed^68,69 and the large photon flux allows determination of position to $\ll 0.6\mathrm{m}$. As the starshade approaches the edge of the 1-m radius control area, thruster firing instructions are sent to it via an S-band radio link. After the thruster firing, in the optimal control scheme,⁷⁰ the starshade is on a ballistic trajectory heading toward the opposite edge of the control area with sufficient momentum to just avoid exiting, after which it falls back and the process repeats.

Formation flight holds a number of challenges. First, the telescope must be kept within the high-contrast shadow region generated by the starshade, accomplished by actively restraining the starshade location so that it remains on the TSSL. Second, the telescope must remain pointed at the target star for observation times that may be as long as weeks. Third, loss of the starshade from the TSSL may occasionally occur, so that a recovery process is needed. Detailed analyses of the formation flying problem with mission-specific assumptions were made^70,71 for the now-cancelled Nancy Grace Roman Space Telescope-starshade Rendezvous Mission (NGRST/SRM) that are relevant here. The concept defined two circular limits within the 2-m diameter design starshade flight region (SFR) [see Fig. 36(b)]. The outer limit $R_{\text{out}}$ is a “do not cross” limit that triggers a compensating thruster firing to move the starshade back toward the center of the SFR. To allow for delays, the radius of this limit is $<1\mathrm{m}$. The inner limit $R_{\text{in}}$ has an even smaller radius that when crossed triggers a thruster firing intended to move the starshade back across SFR to the opposite inner limit. The direction of thrust is tailored to move the starshade back to a position that produces the maximum possible time between thruster firings, that is, the point on the inner limit on the radius pointing in the direction of the starshade acceleration, as shown in Fig. 36(a). The positions of these limits are set based on simulations of the space environment and a model of the formation flying sensor.⁶⁸ The control scheme developed for NGRST/SRM has been tested in a realistic model using Monte Carlo simulations and shown to result in thruster firing intervals $\sim 30\%$ shorter than perfect control would allow. Recent analysis⁷² shows significant increases in thruster firing intervals for particular locations of target stars with respect to the Sun–Earth axis, so there are nuances that have yet to be incorporated into DRM models that may result in reductions in the mass of propellant needed for formation flying.

Fig. 36

(a) Initial path of the starshade in the 2-m circle and the ideal final path against the local SRP and gravitational acceleration. (b) Trigger boundaries for the control system.

The formation flying sensor must provide both the starshade location within the SFR and the pointing error. This pointing error is a combination of telescope pointing error (mainly FGS error) and the pointing direction of the starshade instrument channels. The angle between these two systems will evolve over time as the telescope temperature changes. For the 6-m telescope aperture, the point spread function (PSF) full-width half-maximum (FWHM) is 20.6 mas at a wavelength of 600 nm. Constraining the rms pointing error to be 2 mas, the light within the science core (a circle at the FWHM containing 50% of the light) will be on average 90% of the maximum. Increasing the pointing error to 3 mas rms causes the light in the core to fall to 80% of maximum, so it is important to constrain the pointing error. There are two ways of doing this: internal laser metrology to detect the tilt difference between the FGS and the starshade channel, or direct detection within the starshade channel. For science observations on MOUS or MOVIS, the camera has a sufficient FOV to contain bright stars that can be used to maintain pointing on the target star, but the starshade camera has an FOV of only 8 mas (Table 9), so that field stars will be few, if any. In this case, using direct detection, pointing must be maintained using guide light from the target star. A tilt sensor could be based on the Zernike wavefront sensor concept.⁷³ The sensor produces an image of the residual Airy disk at the center of the starshade shadow, slightly modified by the tilt of the telescope. A new sensor and analysis method⁷⁴ developed from that proposed by Bottom et al.⁶⁹ is capable of detecting the starshade location with respect to the TSSL, together with the telescope tilt. Simulations made for NGRST/SRM show pointing measurement accuracy of $\sim 3.1\mathrm{mas}$ and position measurement accuracy of $\sim 40\mathrm{mm}$ on fifth magnitude stars. With the larger aperture of ATSA, even higher accuracy would be expected.

Table 9

Key features of the instruments.

Over prolonged observation times, Monte Carlo simulations⁷⁰ for NGRST with SRM have demonstrated robust formation flying of the starshade for periods of a week or so and similar qualities are expected for ATSA. These simulations showed very few correction burns: around the 400-s mark on the horizontal axis of Fig. 37. These burns occur when the trajectory reaches the outer trigger boundary shown in Fig. 36. In the extreme case of loss of the formation, an event that did not occur in the simulation, the starshade position can be recovered by switching to detection of the beacon on the starshade science camera and following the normal starshade acquisition procedure.

Fig. 37

Results of a Monte Carlo simulation of formation flying for NGRST/SRM with a realistic (but not yet optimized) sensor and control model. The time between thruster firings is shown on the horizontal axis and the histogram shows the number of bounces (i.e., thruster firings). The typical period between firings is 850 s. To the left correction, burns can be seen at about the 400-s mark. This figure adopted with permission from Ref. 70.

4.6.

Transitions

A starshade imposes some restrictions on observations, because switching from one target to another requires not only slewing the telescope, but also moving the starshade across the sky (a process termed “transition”) to a position between the telescope and the new target, a journey that could take days or weeks. Constraints on the angle made to the starshade by the Sun create an annulus from 40 deg to 83 deg, in which stars are observable. (These angles are conventionally chosen—the smaller angle is set by tolerance for sunlight diffracted from the starshade edges and could be adjusted, whereas the larger angle could be set to 90 deg or more by allowing the starshade to tilt with respect to the starshade-telescope line of sight,⁷⁵ allowing a little more flexibility in observations.) Planning the observations requires an optimization of the traveling salesman problem (TSP) to balance fuel consumption, transit time, and target potential. The Exoplanet Open-Source Imaging Mission Simulator (EXOSIMS)⁷⁶ optimizes the TSP for starshade missions by scheduling observations that are dynamically responsive to discoveries during the simulated mission.^72,77–79 EXOSIMS draws exoplanets from probability distributions of planet properties. The planets are synthesized around stars within 30 pc, and an observing sequence is dynamically simulated. This occurs on a Monte Carlo ensemble of hundreds of synthetic universes. Figure 38 shows one example universe and its observations and starshade path more than 5 years.

Fig. 38

Example of a 5-year observing program with perfect prior knowledge. Synthetic planets, from a broad list of $\sim 950$ potential target stars, are “observed” and considered detected or characterized if the goal SNR is reached. Green points mark observed rocky planets in the HZ, purple other observed planets, including rocky planets, not in the HZ. Gray points mark unobserved stars. Spectral characterizations with the starshade are distinguished by a black edge around the circle marker and are at the tip of a black slew arrow. The white annulus is the region of observability possible for the starshade on day 1826. As the year progresses, the longitude of the annulus moves. The central gray circle with yellow border is the solar “keep out” zone of the telescope. The position of the Sun is labeled “S” and denoted by a gray cross.

Yield results are discussed in detail in Sec. 8, for several different scenarios. In this section, we focus on the operational aspects of observing with a starshade, which are more or less independent of the scenario. At the outset, it is worth pointing out that a great deal of effort has gone into the determination of yield over the last few years.^80–82 Although uncertainties are still large, for telescopes, instruments, and starshades that can be considered credible over the next decades, the number of available rocky habitable-zone planets will be in the tens and not hundreds.

In the starshade-only observing scenario, a blind-search survey is conducted in imaging mode. Once a planet is detected, the starshade remains on the target for spectral characterization. Revisit observations in imaging mode are made at later epochs to determine if the characterized exoplanets are in the HZ. The starshade target list therefore grows throughout the mission and the final yield is dependent on the efficiency and effectiveness of the blind search. The blind search and subsequent orbit determinations are made during a series of starshade maneuvers (transitions). The architecture presented in this paper took an average of 70 transitions with average duration 22 days during a 5-year mission.

Sufficient xenon propellant is carried to provide $\sim 100$ SEP thruster firings (before refueling) to reach starshade velocities up to $50\mathrm{m}{\mathrm{s}}^{-1}$ in $\sim 7$ days, followed by an equally long deceleration phase. In survey mode, the starshade would typically spend only a day or so at each target, whereas in the spectroscopy mode, the observation might last weeks. Additional trade studies of observing strategies and starshade architectures would help find the lightest and most agile starshade configuration that will meet mission requirements. In particular, time-consuming surveys by ATSA would not be required if precursor missions and ground surveys reveal a suitable number of targets with their orbital parameters, in which case the bulk of the mission time would be devoted to spectroscopy and the survey phase minimized. One particular such precursor case is evaluated in Sec. 8, showing that the yield rate accelerates and that prior knowledge has the most significant impact on yield for the starshade-only architecture.

Transition would be initiated after the completion of observations on a science target. Released from the formation, the telescope would switch to another science mode and slew to another target, and the starshade would initiate its transition. With the set of SEP thrusters, the starshade can move in any direction. Using the biprop thrusters, the starshade’s rotation is stopped for the transition and restarted at the required orientation at the next target. Over the duration of the mission, this uses approximately half of the biprop fuel. Continuous thrusting is used throughout the transit, with the deceleration phase immediately following the acceleration phase. Navigation is by dead reckoning; that is, the starshade’s location is only approximately known upon arrival at the new TSSL and the starshade would then be located by telescope observations. The final location of the starshade depends on a number of parameters⁸³—the starshade mass, which varies as fuel and propellant are used, the direction of thrust during acceleration and deceleration, gravity and SRP vectors, and initial positions of the starshade and telescope. Nano-g accelerometers with $2\mathrm{ng}{\mathrm{Hz}}^{-1/2}$ noise levels have been developed⁸⁴ and can be used to estimate the starshade trajectory under the thrusters. Starshade mass, gravity, and SRP effects can be estimated from the formation flying data at the previous target, plus a knowledge of the telescope and starshade’s position in space relative to Earth, Sun, and Moon, so that accelerations and positions can be continuously estimated. Anticipating the starshade’s arrival at the new target star, the telescope turns to observe the target and uses the wide field camera MOVIS to locate the starshade beacon.

Assuming typical 22 deg transitions, for the starshade to fall within the FOV of MOVIS requires trajectory direction accuracy of better than 0°.14. Assuming the starshade accelerates under the thrust of two SEP thrusters, the acceleration is $\sim 8\mu \mathrm{g}$ and with the noise from just one accelerometer, the rms trajectory error is $<0^{°}.02$. If this were the only error, then taking into account the same error in the measured acceleration, the starshade will arrive within an approximately spherical region with rms radius of $\sim 1^{\prime }$ seen from the telescope. Various factors perturb the trajectory—for example, free fall under gravity is not detected by the accelerometers—but these factors and the influence of radiation pressure ($<1\mu \mathrm{g}$) are calculable with a knowledge of the orbital positions of the telescope and starshade. Flinois et al.⁸³ found that the dominant contributors to final position uncertainty are the initial velocity uncertainty from the retargeting burn and the SRP, owing to the large area of the starshade and its variable presentation angle to the Sun. For shorter cruise (transition) periods of 7 days, the error in the final position is $<5\%$, using a conservative model. Note that Flinois’s analysis considered conventional thrusters rather than SEP: the error in the estimated trajectory is likely to be different for ATSA and further analysis is required. In the absence of that we assume that the starshade is likely to be found within the FOV of MOVIS ($3^{\prime }\times 3^{\prime }$), but if necessary a raster search in a 10′ region using the telescope’s 4 N monoprop thrusters will suffice for detection.

Once the beacon is detected, the starshade is guided toward the line of sight to the target star via data sent from the telescope on the S-band link, while pointing adjustments are made to the telescope as necessary. Ultimately, with the star centered on the focal plane of MOVIS, the starshade comes within the FOV of the chosen starshade guide camera channel ($\ge 7^{″}$ diameter) and the telescope slews to center the starshade instrument FOV on the target star, thus capturing the starshade beacon on the starshade instrument cameras.

6.1.

Overview

The two main aims of the optical instrument designs are to maximize optical throughput without compromising diffraction-limited performance and to bring certain detector surfaces out as near as possible to the side of the AMS structure open to space to facilitate passive detector cooling. This has the benefit of eliminating the need for heat pumps and associated vibration and reducing complexity. Two instruments provide capabilities for general astronomy and astrophysical investigations: the MOUS (covering 115 to 315 nm) and the MOVIS (covering 320 to 5000 nm). Both instruments can also function as cameras. The other instrument, EXPRESS, is specialized for exoplanet and disc studies; the starshade instrument (EXPRESS) functions in concert with the starshade spacecraft and is particularly suited for spectroscopy. Specifically:

In addition, there is a fine guidance instrument that has two optically identical channels (though folded differently) and focal planes. Other instrument types that are or will be directly useful for exoplanet studies are in development and might be applied to the segmented telescope design. Some of the options are discussed below (Sec. 6.6).

The optical system views the sky through six separate fields, as shown in Fig. 39. The optical configuration of each channel is either a three or four-mirror afocal telescope with of order $140\times$ angular magnification (varying by channel) followed by reimaging optics. The afocal telescope has a common primary and secondary in all channels, followed by an optical switchyard consisting of fold mirrors that divert the light to the different channels and separate subsequent reimaging optics. Figure 40 shows the optical layout of the full instrument system behind the AMS (instrument and switchyard enclosures are not shown). The optical and mechanical designs were developed together to ensure practical packaging and clearances within the available space. Table 9 summarizes key features and current modeling assumptions of all the instruments.

Fig. 39

(a) Arrangement of the instrument fields of view (sizes not shown to scale). The MOVIS near-UV channel views a different field than the other MOVIS channels. Otherwise, the instruments split the wavelength channels internally. (b) Optical switchyard from which light is directed to the instruments. Optical components are mounted within an enclosure attached to the AMS with bipods.

Fig. 40

View from behind the AMS showing the optical layout. To the right, NIR and MIR focal planes are brought out as close as possible to the cool side of the bus so as to maximize the heat flow to the exterior radiators. To the left, the remaining focal planes have less stringent cooling requirements and can be cooled with longer conductors. In places where optical paths appear to cross, the components are at different distances from the AMS. Instrument enclosures are not shown but can be seen in Fig. 25.

6.2.

Multiobject Ultraviolet Spectrograph

MOUS is designed for high-resolution spectroscopy from 115 to 315 nm. Its capabilities include multiobject grating spectroscopy, UV imaging, and spectroscopy using bandpass filters. We show thin transmissive filters of base material LiF, which can operate to below 115 nm,⁸⁵ but an alternative would be plane reflective filters and a consequent fold path, depending on analyses and throughput trade-offs. A schematic diagram is shown in Fig. 41 and the corresponding optical layout is shown in Fig. 42. To maximize throughput, the primary and secondary mirrors (in fact, all the mirrors in MOUS’s path) are coated with aluminum, protected by a layer of ${\mathrm{MgF}}_2$. Detection of light across this range would be accomplished using a large ($>\mathrm{36,000}\times \mathrm{26,000}$ pore) microchannel plate (MCP) detector, which is a sensitive low-noise electron-multiplying device. Its GaN photocathode, deposited using the atomic layer deposition technique, yields best performance with quantum efficiency near 80% at the shortest wavelengths.⁸⁶ Selection of objects within the FOV is made using an MSA—a large array of individually commanded shutters.

Fig. 41

Schematic of MOUS showing the principal components.

Fig. 42

Optomechanical layout of MOUS showing the beam entering from the telescope secondary, the tertiary, and quaternary mirrors and the grating wheel. Optionally, optical filters can be placed into the beam before the focal plane.

MOUS can be used simply as a camera and optionally, filters can be inserted for use in imaging mode. It also contains a number of gratings covering the ranges shown in Table 10, with resolution up to 60,000. MOUS accepts light from a field centered 0°.074 off the primary mirror axis, encompassing an FOV of $3^{\prime }\times 3^{\prime }$. A removable MSA can be positioned where the primary–secondary combination forms an $f/16$ Cassegrain focus, enabling objects in selected areas of the FOV to be included or excluded. The MSA consists of a set of four units, closely butted together, of a version of the planned next-generation (NexGen) electrostatically actuated type,⁸⁷ with $420\times 210$ apertures each and $840\times 420$ apertures total. Here we are assuming a custom version, slightly larger than the proposed CETUS⁸⁸ NexGen version (which is $365\times 171$). Apertures will be $180\mu \mathrm{m}\times 80\mu \mathrm{m}$ in size on $200\mu \mathrm{m}\times 100\mu \mathrm{m}$ pitch; each component has about 40% more operating area than the MSAs designed for NIRSpec⁸⁹ ($365\times 171$ each of four units) but is more compact in overall form. The reason for using a set of four smaller arrays is to make a best-fit match to the curved Cassegrain focus; each quadrant of the MSA will be a separate flat array, slightly tilted to match the best-fit focal surface. The maximum diffracted PSF size (50% encircled energy diameter) at the MSA is $17\mu \mathrm{m}$ at 300 nm wavelength.

Table 10

MOUS: MSA and grating resolutions.

Table 10 shows the main features of the instrument. Following the MSA, tertiary, and quaternary mirrors create a collimated beam at $162\times$ angular magnification from the primary mirror, with a pupil being formed at the grating (or plane mirror) carried by the grating wheel. The collimated light reflected from the grating is focused onto a curved FPA detector by a fifth mirror.

Figure 43(e) shows the Strehl ratio for the UVS imager. The imperfections of real optics are omitted. These optics would be highly polished and accurately finished to minimize additional WFE. We anticipate that performance would be further improved by additional design work.

Fig. 43

Strehl ratio across the fields of view (axes scaled in deg) for MOVIS (a)–(d) four camera channels and (e) MOUS. The well-corrected field area, i.e., the fraction of the 3′ × 3′ focal plane area which is diffraction limited, is shown for each channel, measured at wavelengths 3098, 1190, 692, 366, and 400 nm, respectively.

6.3.

Multiobject Visible-Infrared Spectrograph

MOVIS is a general-purpose spectrograph and camera providing imaging and spectroscopy modes over four bands from the near-ultraviolet (320 nm) to the MIR ($5\mu \mathrm{m}$). The principal components are illustrated in Fig. 44. The three channels for visible light, NIR, and MIR wavelengths share the same 3′-square FOV, whereas the near-UV channel has a separate FOV, enabling a higher throughput beam path. An MSA is provided for use in spectroscopy mode or to facilitate observations of fainter objects in bright fields. Sets of filters based on the Hubble WFC3 sets⁹⁰ are provided for spectroscopic observations in the UV, Vis, and IR channels. Each filter set also includes one or more zero-deviation dispersing prisms, which can be used in series with another filter to select a spectral resolution and band of interest. Additionally, a set of filters is provided in the MIR channel. This instrument is intended for general use on objects both inside and outside the solar system and provides $2.5\times$ better resolution than Hubble with more than 6 times as much collecting area.

Fig. 44

Schematic of MOVIS showing the principal components. The UV channel has a separate field. The Vis/IR channels share the same beam train before a final split and share the same field as the MIR channel.

MOVIS has a UV band covering 320 to 450 nm, a visible band (Vis) covering 450 to 950 nm, a NIR band covering 950 to 2400 nm, and an MIR band covering 2400 to 5000 nm. The optical layout of the instrument is shown in Fig. 45. To provide a multiobject spectroscopy facility, the Vis and NIR channels share a common MSA (not the MOUS MSA, but a separate one within MOVIS) that is removable for imaging purposes. The MSA consists of a set of four units, closely butted together, of the NexGen type with $1680\times 840$ apertures total: again, $180\mu \mathrm{m}\times 80\mu \mathrm{m}$ in size on $200\mu \mathrm{m}\times 100\mu \mathrm{m}$ pitch. Each component has more than $4\times$ the optical area of the component MSAs designed for NIRSPec. The UV channel views a separate field from the Vis/NIR/MIR channels and does not have an MSA, allowing the channel to have fewer mirrors and higher UV transmission than if it shared the optics with the Vis/NIR/MIR channels. The Vis, NIR, and MIR channels observe the same $3^{\prime }\times 3^{\prime }$ field simultaneously through dichroic beamsplitters. Thus extremely broad band (450 to 5000 nm) imaging and spectroscopy on a chosen field can be achieved in a single observation. The switch between imaging and spectroscopy modes in Vis and NIR is implemented using flip-in grisms located in the filter wheel assemblies, together with the insertable MSAs. The spectral resolution when in spectroscopic mode is $R=2000$ in Vis and NIR channels. All channels are equipped with filter wheels for use when imaging. Additional low- or medium-resolution spectroscopic capabilities could readily be provided in the UV and MIR channels.

Fig. 45

Optical layout of MOVIS, showing the beam entering from the telescope secondary, the tertiary and quaternary mirrors and the grating wheel. Optionally, optical filters can be placed into the beam before the focal plane.

The MOVIS UV and Vis channels would utilize deep-depleted, delta-doped charge coupled device (CCDs) with $12\text{-}\mu \mathrm{m}$ pixel size, in a $3\times 3$ mosaic, providing a total of $12\mathrm{k}\times 12\mathrm{k}$ pixels. The FPA would be cooled to 153 K. The NIR channel would utilize a low-noise hybrid HgCdTe/CMOS detector, such as the Teledyne© H4RG, with $10\mu \mathrm{m}$ pixels in a $4\mathrm{k}\times 4\mathrm{k}$ format.

The optical design of the MOVIS UV channel includes aspheric tertiary and quaternary mirrors that create a collimated beam, demagnified by about $144\times$ from the primary mirror. Following the quaternary, a three-mirror imager (utilizing rotationally symmetric aspheric shapes) forms a $f/41$ final focus. The RMS WFE across the $3^{\prime }\times 3^{\prime }$ FOV is $<39\mathrm{nm}$.

In the Vis/IR channels of the MOVIS, as in the UV channel, tertiary and quaternary mirrors create a collimated beam at about $144\times$ angular magnification from the primary mirror. However, the optical design of the rest of the Vis and IR channels is more complex than the UV channel, due to the need for an MSA. The Cassegrain focus after the telescope secondary could not be used for the MSA in these channels because the focus there (further off-axis than the MOUS FOV) is not well corrected. The tilt and decenter and shape of the telescope secondary were optimized for high performance specifically at the MOUS MSA FOV and therefore the performance at the Cassegrain focus of the MOVIS NIR/Vis FOV was not adequate for an MSA. Therefore, after the Vis/NIR quaternary, a four-mirror focuser creates a well-corrected telecentric $f/33$ focus where the MOVIS MSA is located. The MSA is followed by the inverse of the focuser, creating another collimated beam. A dichroic beamsplitter is placed in the collimated beam to reflect Vis and transmit NIR light. Following the beamsplitter in each channel is a filter wheel assembly that holds several wheels carrying filters or dispersing elements. After the filter assembly is the final focusing section. In the NIR channel, this is an $f/20$ refractive group consisting of five rotationally symmetric elements of common near-IR materials (zinc sulfide, zinc selenide, and fused silica). This refractive solution is compact and is adequate to correct chromatic aberration. In the Vis channel, the $f/41$ focusing group consists of three mirrors (one of which is a rotationally symmetric aspheric and two of which are Zernike aspherics). Figure 43(a)–(d) shows the Strehl ratios and well-corrected field fractions for the four MOVIS imaging channels.

6.4.

EXoPlanet Range Extended StarShade Instrument

EXPRESS provides separate UV, visible, near-IR, and mid-IR channels sharing the same 8″-class diameter FOV, as shown in Fig. 46. Table 11 shows the operating regions for EXPRESS. In each case, two of the instrument channels are used for science (since the starshade bandwidth is wider than the bandwidth of the individual channels) and one channel is used for guiding, with an optional channel choice shown in brackets. All channels can be used in an imaging guider mode and the Vis and NIR channels can be used in imaging or narrower 1.1 to 1.8 arc sec field spectroscopic modes. A typical operational configuration might be to utilize the UV channel in guider mode, with the pupil imaging lens (PIL) inserted in the beam to create a pupil image on the UV detector, whereas the NIR and Vis channels perform imaging or spectroscopy. As an alternative in this particular mode, the guide signal can also be picked up in the MIR channel, which may be helpful when observing cooler stars. Selection of modes within each channel is done using insertable devices: selector mirrors for the Vis and NIR channels to send the light to the imaging FPA or through the respective IFS optics; PILs in the IR and UV channels and an insertable prism in the UV channel.

Fig. 46

Schematic of EXPRESS. Light from the telescope is split into four channels using dichroic beamsplitters. All channels share the same FOV and can be operated as imagers or as starshade guide channels via insertable PILs. For spectroscopy, the Vis and NIR channels each carry an IFS and the MIR channel carries filters.

Table 11

Starshade operating bands.

The optics common to the EXPRESS channels consist of the telescope primary and secondary mirrors, and the aspheric tertiary and quaternary mirrors that create a collimated beam, magnified by $116\times$ (angular) from the primary mirror. In small-beam space, the field angular diameter is only 0°.28 total, so a simple off-axis paraboloid is sufficient to form a high-quality $f/80$ converging beam, with rms WFE of up to 27 nm across the field. This $f/80$ beam propagates directly to the FPA in the UV path and is the input beam to the Vis, NIR, and MIR paths in which the final $f$ number is smaller.

The four EXPRESS channels share the same far-field FOV and are separated by dichroic beamsplitters. The first beamsplitter reflects the UV to its $f/80$ focus and transmits the Vis, NIR, and MIR. The second beamsplitter reflects the Vis and transmits the NIR and MIR. Following the Vis/IR beamsplitter, in reflection, is a weak doublet of radiation-resistant glasses that converts the $f/80$ beam emerging from the paraboloid to the $f/70$ focus required for the Vis channel. The RMS WFE in the Vis channel is $<30\mathrm{nm}$ across the 450- to 1000-nm band. Following the Vis/IR beamsplitter in transmission, the beam crosses to the opposite side of the spacecraft bus, which is the cold side. A conic mirror collimates the beam and another dichroic beamsplitter in collimated space separates the beam into NIR and MIR paths. In both IR paths, a refractive doublet makes the final focus onto the imaging FPAs. The RMS WFE at the imaging FPAs is a maximum of 66 nm in NIR and 80 nm in MIR, yielding excellent image quality across both bands. In the NIR path, a switch-in mirror diverts the light to an IFS.

In the EXPRESS paths described, flip-in elements have been designed for other modes besides far-field undispersed imaging. In the UV path, a PIL may be inserted that forms an image of the primary mirror on the FPA, allowing starshade guiding. Also in the UV path, a prism (carried by the same mechanism as the PIL) may be inserted to perform $R=5$ dispersion. In the NIR path, a PIL may be inserted to create an image of the primary mirror when using this channel for starshade guiding.

The Vis and NIR channels also have IFS modes with separate FPAs, accessed by flipping in a flat mirror in the image spaces ($f/71$ for Vis and $f/51$ for NIR) to access two-mirror relays that magnify the images onto lenslet planes. Following each lenslet plane is a collimator, prism and focuser to create dispersed images at the FPAs. The NIR IFS relay optics between lenslet and FPA consist of back-to-back six- or seven-element objectives, with a zinc sulfide prism ($R=40$) between them in collimated space. The overall magnification is 0.7. RMS WFE in the NIR IFS varies with wavelength but has a worst case value of 98 nm. The Vis IFS relay optics between lenslet and FPA consist of back-to-back three-mirror objectives, with an NBK7 prism ($R=140$) between them in collimated space. The overall magnification is 1. RMS WFE in the Vis IFS varies with wavelength but has a worst case value of 97 nm. DoF exist to improve the performance in the final design.

The present design features filter-based imaging spectroscopy in the MIR as a low-resolution, high signal-to-noise ratio (SNR) option but there is space in the instrument bay for a specific spectroscopic EXPRESS MIR channel. Recent work⁹¹ has reaffirmed that a Fourier transform spectrograph (FTS) can compare favorably against an IFS in the noise conditions likely to be encountered at longer wavelengths. An FTS also offers dynamic flexibility in the choice of spectral resolution $R$. A broad trade study between filter sets, FTSs, and IFSs, which considers source and background SNRs, candidate detector characteristics, and in-depth analysis of the ideal values of $R$ for target species detection, could lead to the inclusion of an EXPRESS MIR spectrograph channel.

6.5.

Fine Guidance Instrument

The FGS enables accurate pointing on the target star using field stars in two regions of the sky when the starshade covers the target. The $1\sigma$ raw angular detection accuracy⁶⁸ in each of the two channels is approximately $\lambda {(\pi d\sqrt{N})}^{-1}$, where $N$ is the photon count, $d$ is the 6-m aperture diameter, and $\lambda$ is the wavelength (visible band). Dark current, read noise, and thermal drifts will affect this figure, but with an electron-multiplying CCD (EMCCD) detector and a stable thermal environment (the case here), submilliarcsecond accuracy can be assumed even on relatively faint guide stars of 15 mag. The two FGS channels can be seen in Fig. 40, labeled “Guiders” and the schematic layout is shown in Fig. 47. A scan mirror in each channel allows selection of field stars and the FOR is sufficiently large to find guide stars over more than 95% of the sky.

Fig. 47

Schematic of topologically identical guide channels, which take widely separated views of the sky. Scan mirrors enable selection of guide stars within a 186″ FOR.

6.6.

Potential Additional Exoplanet Instrumentation

The ATSA telescope platform could potentially be augmented by other exoplanet science instruments. Unlike starshades, for which the mission DRM must be carefully prescribed, coronagraphs provide a flexible and agile exoplanet observing capability, most useful for exoplanet discovery but also capable of spectral characterization. This is provided that both broadband starlight suppression and high exoplanet throughput can be simultaneously achieved with coronagraphs on the ATSA telescope. At the current state of the art, high-contrast ($\simeq {10}^{-10}$) coronagraphs are not well-suited for use with apertures having central obscurations^92,93 and spiders, such as are found on NGRST. Segmented apertures, however, which also pose difficulties for many coronagraph designs, can work satisfactorily with apodized coronagraph schemes, especially when combined with a vortex mask. Apertures having low $f$ numbers are undesirable, owing to the problem of polarization crosstalk⁹⁴ caused by differential phases induced between the polarizations upon reflection from mirrors. HabEx 4.0H employed an $f/2.5$ off-axis design with a monolithic primary mirror, thus avoiding these issues, but it is clear that to provide the largest possible apertures in space, segmented apertures will need to be employed, just as on the ground. Also shorter telescopes and hence smaller $f$ numbers are desirable from an engineering standpoint.

Can other types of instrument be deployed with the ATSA aperture? For example, high-precision astrometry using diffracting pupils applied to the primary mirror⁹⁵ is a technique not yet applied to space, but with projected astrometric accuracy well below $0.1\mu \mathrm{arc}$ sec, a 6-m aperture would be capable of detecting Earth-size exoplanets at 12 pc (producing $\sim 0.25\mu \mathrm{arc}\sec$ stellar motion).⁹⁶ A recent study⁹⁷ is showing potential for this technique with HabEx 4.0, where the diffracting pupil is a removable surface downstream of the OTA. For a metrology-stabilized segmented aperture, such as ATSA’s, the technique would be worth studying.

Another recent development is the pupil-plane vortex fiber nuller,⁹⁸ which can be considered the smooth limit of the multiaperture nulling configurations proposed for Terrestrial Planet Finder Interferometer (TPF-I)⁹⁹ and Darwin.¹⁰⁰ This technique^101–103 is soon to be tested on the segmented Keck aperture, providing a useful data point for ATSA. Note that when used for nulling, the telescope aperture is capable of detection well within the usual coronagraph limit.¹⁰⁴ A cross-aperture single-baseline nuller has an IWA equal to $\lambda /4b$ (where $b$ is the interferometric baseline) and this is equal to between 1/4 and 1/3 $\lambda /d$, approximately an order of magnitude closer to stars than a full-aperture coronagraph (IWA $\sim 2.5\lambda /d$). Thus nulling configurations, which had fallen out of favor post-TPF, may yet make valuable contributions to exoplanet science by combining smaller IWAs, as demonstrated by the Palomar fiber nuller,¹⁰⁵ with all the agility of coronagraph-based techniques. Another addition to the nulling stable is the grating nuller, which combines naturally achromatic beam combination with ease of fringe rotation.¹⁰⁶ Opportunities to develop and test these new techniques may eventually result in the development of alternatives to conventional coronagraphs and starshades.

In addition to these alternatives, one challenge in coronagraph technology development is to develop high-contrast instruments capable of ${10}^{-10}$ diffracted starlight suppression over broadbands while maintaining high throughput. For example, coronagraph core throughput (defined as the fraction of planet light captured in a region $0.7\lambda /\mathrm{D}$ in radius) in the NGRST-CGI instrument (when using the Hybrid Lyot masks) falls below 5%—compared to the 34% core throughput of the telescope itself—owing partly to the negative effects of the obscured aperture.^107,108 While discussion of the potential for coronagraphy on segmented telescopes is outside our scope, the addition of a high-performance coronagraph to ATSA would (potentially) enhance its capabilities for exoplanet studies. Concepts for an apodized vector vortex designed for the ATSA aperture geometry are being developed.¹⁰⁹ Without minimizing the difficulties of incorporating a coronagraph, an active PM, as part of a system of two downstream DMs, would considerably reduce the initial WFE and hence the energy subsequently spread into higher spatial frequencies as part of WFC. Mid-spatial frequencies are particularly challenging because the scattered light appears close in.⁹³

An ideal coronagraph solution for segmented telescopes has not yet been identified. Among the types being studied are binary and gray scale apodizer masks that would be inherently achromatic and provide broadband starlight suppression with reasonably high exoplanet light throughput. Furthermore, the vortex coronagraph mask offers significant advantages compared to the Hybrid Lyot design (one of two coronagraph types employed in NGRST-CGI) with its much greater tolerance to low-order aberrations, such as tilt.⁹³ These low-order aberrations dominate coronagraph performance when telescope motion, thermal effects on the optical train, and vibration are considered. Detailed sensitivity analyses of apodized vortex coronagraphs for unobstructed hexagonal segment apertures are made in Ref. 93. The same approach to coronagraph design could be applied to the centrally obstructed, segmented ATSA aperture. We note, however, that high-contrast coronagraphic observations will prove particularly challenging in the UV whatever the entrance aperture geometry, where polarization-induced aberrations and throughput limitations are amplified, whereas wavefront stability and stray light requirements get more stringent. Where high-contrast spectral observations of exoEarths are required in the UV, starshades may be the only solution.

In terms of science, the provision of complementary techniques has been shown on HabEx 4.0H² with its starshade and its coronagraph, to roughly double the exoplanet yield. With segmented telescopes likely to become the norm in space in the future, further study of these possible techniques should be rewarding.

8.1.

Yield Modeling Approach

EXOSIMS⁷⁶ performs full, end-to-end mission simulations of exoplanet direct-imaging missions. Every aspect of the mission, from the orbital position of the spacecraft, to the characteristics of its optical system, to the target stars and their planet populations, and their time-varying positions, is described parametrically. Full missions are scheduled using specific descriptions of observing rules, and each individual observation is evaluated on a specific sample of simulated exoplanets drawn from the governing population. Monte Carlo ensembles of mission simulations are generated with different samples of planets and orbits, and these are then analyzed to calculate distributions of mission performance metrics. Full mission simulations allow for the exact inclusion of dynamical constraints and allow for simultaneous calculation of a wide range of scientific and engineering metrics of interest (e.g., spectral characterizations and fuel use).

8.2.

Astrophysical Inputs

The astrophysical assumptions and inputs are summarized here and discussed in greater detail in the Exoplanet Exploration Program Office’s Standard Definitions and Evaluation Team (ExSDET) Final Report.⁸¹ Uncertainties in yield are dominated by uncertain knowledge of astrophysics inputs, particularly for exoplanet occurrence rates and the brightness of exozodiacal light.

Exoplanet occurrence rates were based on the EXOPAG SAG-13 power-law model of Kepler data,¹¹¹ as modified by Dulz et al.¹¹² for planets with larger masses and orbital radii. In particular, the occurrence rate for Earth-like planets is taken to be 0.24. Exo-Earth candidates (EECs) were assumed to be on circular orbits and to reside within the conservative HZ, spanning 0.95 to 1.67 AU for a solar twin.¹¹³ EECs span radii ranging from $0.8a^{-0.5}{R}_{\oplus }$ to $1.4R_{\oplus }$, where $a$ is the semimajor axis for a solar twin, and $R_{\oplus }$ is the Earth radius.

The stray light from binary stars in the final image plane was estimated¹¹⁴ and included as an astrophysical noise source in exposure time calculations. The solar zodiacal cloud brightness was estimated as a function of wavelength and ecliptic latitude and longitude by adapting and interpolating data from published tables. ¹¹⁵ EXOSIMS specifically schedules each observation, enabling it to compute the zodiacal brightness based on the target’s ecliptic coordinates on the date of the observation. The exozodiacal light levels were drawn from the recent results of the Large Binocular Telescope Interferometer survey of exozodiacal dust, represented as a probability distribution with a median brightness level three times higher than in the Solar system case.¹¹⁶

EXOSIMS uses the ExoCat-1 catalog of nearby main sequence stars.^117,118 Any necessary but missing photometric information for targets is optionally synthesized by interpolating over Eric Mamajek’s Mean Dwarf Stellar Color and Effective Temperature Sequence.¹¹⁹ ExoCat-1 is further modified to include the physical characteristics of any multiple systems (delta magnitude and separation) from the Washington Double-Star catalog, maintained at the U.S. Naval Observatory, allowing modeling of the amount of starlight contributed by any known nearby stellar companions.

The telescope–instrument combinations are modeled parametrically using the values presented in this paper.

8.3.

Observing Scenario

The starshade-only observing scenario begins with the starshade performing a blind search survey. When a planet is discovered, the starshade remains on that target to perform a spectral characterization. The starshade returns at later times (“epochs”) for follow-up imaging for orbit determination. The integration time is set to reach an SNR of 7 for broadband imaging and an SNR of 10 per resolution element for spectroscopy, using the brightness of the planet determined by initial imaging and assuming a Lambertian phase function.

Follow-up imaging-mode detections contribute to orbit determination. For the cases studied, not all targets that are spectrally characterized received all the requisite orbit determination observations, due to practical timing constraints for observing with the starshade. The TSP optimization cost function includes terms for the EEC search completeness around each target, transition distance, revisits for orbit determination and the number of potentially missed targets during the blind search survey. The spectral characterizations take highest priority. The cost function coefficients used here were achieved with a preliminary tuning and could be further refined. The cost function coefficients should be retuned for changes in observing scenario and architecture, particularly starshade-telescope separation, mass, propulsion type, and fuel mass.

8.4.

Precursor Knowledge

In the absence of a coronagraph or a second smaller, more agile starshade focused on rapid broadband exo-Earth detection, precursor knowledge of HZ rocky planets would rely on prior surveys using precision RV measurements, astrometry, or ground-based direct imaging. Ground-based ELTs equipped with extreme adaptive optics and high-contrast starlight cancellation systems may have the capability to detect Earth-like planets around a dozen M stars,¹²⁰ but likely not around the solar-type stars targeted by ATSA. Astrometry would need to reach microarcsecond level precision, which is only accessible from space (and at least $20\times$ better than Gaia⁵² will provide). The Space Interferometry Mission^121,122 had the potential to reach as many as 65 exo-Earths with $\sim 1\mu \mathrm{as}$ precision but was canceled. Other ideas, e.g., diffractive pupil astrometry,¹²³ are only just beyond the concept phase. For the foreseeable future then, the leading technology for detecting and measuring the orbits of exo-Earths around Sun-like stars is ground-based extreme precision radial velocity (EPRV) measurements.¹²⁴ The required precision is $\sim 10\mathrm{cm}/\mathrm{s}$ (with a few cm/s stability over many years), which is significantly better than the 1-m/s routinely achieved by current ground-based RV instruments. Recognizing this gap and the high impact of precursor knowledge on the design and science yield of any future exo-Earth direct characterization mission, the 2018 National Academy of Sciences (NAS) Exoplanet Science Strategy report ¹²⁵ recommended the development of EPRV measurements as a critical step toward the detection and characterization of exo-Earths. In response to that recommendation, NASA and NSF commissioned an EPRV group to recommend a ground-based program architecture and implementation plan to achieve the EPRV goal intended by the NAS. Only the next 5 to 10 years of EPRV work will tell if such measurements are achievable.

In the baseline observing scenario described above, no prior knowledge of EECs—nor of any other planet types—is assumed around the targets and the burden of a blind search survey falls on the mission. For the opposite extreme, we consider a case in which perfect knowledge of the location and orbits of the exo-Earths exists around all target stars. In that extreme case, no blind search is necessary and only spectral characterizations are performed. This perfect prior knowledge case investigates the upper bound set by the scheduling of the starshade for spectral characterizations and defines the capability of the instrument to exhaust targets within the maximum integration time criterion of 60 days per spectral observation. Having any precursor knowledge of EECs, either from ground- or space-based surveys, would produce EEC characterization yields within these two bounds. We evaluate one particular precursor case: detection of EECs with EPRV with sensitivity $3\mathrm{cm}{\mathrm{s}}^{-1}$. EPRV sensitivity degrades with increasing stellar temperature. We incorporated EPRV precursor knowledge into EXOSIMS: each synthesized planet around a given star is tested against a heuristic of the EPRV sensitivity for that particular star and planet mass.¹²⁶ If the planet is detectable by EPRV, it is designated for spectral characterization at mission start. The null results of EPRV are not used; the blind search survey is conducted on all targets without EPRV precursor planets.

8.5.

Yield Results

The yield was calculated for the no-prior knowledge, perfect-prior knowledge, and EPRV-prior knowledge cases. The yield simulations were performed with synthetic planets of all the Koppurapu planet types¹²⁷ drawn from the Dulz occurrence rates,¹¹² using an ensemble of 100 randomly drawn universes for each of the three prior knowledge cases. The mission rules prioritized exo-Earths when scheduling observations, and the yield of non-exo-Earths is incidental during the exo-Earth-centric observations. Greater yield of non-exo-Earths could be achieved with different mission rules. The yield is defined as the average number of exoplanets that were spectrally characterized to $\mathrm{SNR}=10$ with spectral resolution of 140 over a 108% bandwidth ranging from 300 to 1000 nm.

Figure 4 shows the cumulative number of exo-Earths spectrally characterized by the starshade over mission elapsed time. The upper bound set by the perfect-prior-knowledge case is 33 spectrally characterized EECs. The targets are exhausted in an average of 4.5 year. Extending the mission an additional year produces an average of 0.3 more characterized EECs. The conclusion is that the ATSA starshade architecture is target-limited and a corollary is that a slightly larger telescope aperture would provide access to more targets to leverage use of the starshade for the full five years of the mission.

At the other extreme, a blind search with the starshade uses about 65 transitions to yield an average of three characterized EECs. With EPRV precursor knowledge, the starshade benefits dramatically, raising the yield to 10 EECs and accelerating the time to half the yield from 641 to 214 days. Based on these yield results obtained for visible wavelength observations, the separation angle of the observed exo-Earths at quadrature was calculated and used to assess how many of these exo-Earths would still be observable given the IWA of the three infrared bands. These results are summarized in Table 12 and annotated in Fig. 4.

Table 12

Number of exo-Earths characterized and time to achieve 50% yield for different scenarios.

The yield of the exoplanets by Koppurapu type is shown in Fig. 48 for the perfect-prior case, in Fig. 49 for the EPRV-prior case, and in Fig. 50 for the no-prior case, observed in the visible. The perfect-prior case observed an average of 31 stars, each one having at least one exo-Earth. The no-prior case, utilizing a blind-search survey, observed an average of 53 stars, thereby having higher yields for sub-Neptunes and gas giants. The EPRV-prior case observed an average of 22 stars, fewer stars than the blind search. It resulted in higher exo-Earth and rocky planet yields but lower sub-Neptune and gas giant yields than for the no-prior case.

Fig. 48

In the perfect prior case, the starshade performs spectral characterizations on all exoplanet systems with exo-Earths and only those systems. The yield of other planet types characterized concurrently with the exo-Earths is shown for five planet types and their respective thermal zones¹²⁷: small rocky, large rocky, sub-Neptune, Neptune, and Jupiter-like types. Exo-Earths are a subset of warm, rocky-type planets.

Fig. 49

In the case of prior knowledge from an EPRV instrument with $3\mathrm{cm}{\mathrm{s}}^{-1}$ precision, the starshade performs spectral characterizations on all exoplanet systems with known exo-Earths and conducts a blind-search survey on the rest of the target stars.

Fig. 50

In the no-prior case, the starshade performs a blind-search survey in broadband imaging mode to SNR = 7. When a planet is discovered, the starshade remains on the target and performs spectral characterization. The starshade revisits systems with discovered planets at multiple later epochs to image the systems and determine the planet orbits to discern which, if any, reside in the HZ.

The planet yields and average number of stars observed are summarized in Table 13. As expected from previous analysis,⁸⁰ the number of exo-Earths that can be spectrally characterized by the ATSA starshade is a strong function of prior knowledge. In this table, the temperatures and Kopparapu planet types are aggregated into rocky planets ($0.5R_{\oplus }<R<1.75R_{\oplus }$), sub-Neptunes ($1.75R_{\oplus }<R<3.5R_{\oplus }$), and gas giants ($3.5R_{\oplus }<R<14.3R_{\oplus }$). Within each set of planet types, the topmost row indicates the total number of planets seen in that set. Subsequent rows show the number of those same planets that can be observed in the longer wavelength bands. Thus while $\sim 1/3$ of the total observable rocky planets are observable in band IR1, large, gaseous planets can be observed in all bands.

Table 13

Expected yield by planet type and wavelength range for different scenarios.

Utilization of recent work^72,79 on higher fidelity starshade transition and formation flying dynamics models in EXOSIMS could reduce the required fuel mass, which are anticipated to increase the yields by 15% or more. Additional optimization of the blind search, tuning of the TSP cost function coefficients and refinement of the architecture could further increase exo-Earth yields by 10% or more.